Some of the potential positives have already been stated. In addition to those, there are several locations added to the game. These include but are not limited to Fort Dawnguard in Dayspring Canyon ESE of Riften(north of Stendarr's Beacon), Castle Volkihar, the Soul Cairn(a plane of Oblivion) and the Forgotten Vale(a large outdoor area). Besides the Dawnguard quest line, there is a sort of mini quest line that starts after reading a copy of Aetherium Wars(a book added by the DLC to various world locations). At the end of the quest you will be able to create one of 3 unique Dwemer artifacts. One of those in particular can be used in a variety of ways to benefit your character. It should be said that if you want to get anything better than the basic crossbow(equal to a daedric bow in damage and double improved with steel smithing btw) you will need to side with the Dawnguard in the DLC quest line and not the Volkihar vampire clan.
Now for the potential downsides.
Vampires will randomly attack cities and towns(usually at night, but it can happen during the day), and the results of these attacks can lead to the death of named NPCs such as merchants and quest givers. They mostly vary from a strong vampire with a few thralls to a vampire with a few death hounds, but can include more than one vampire. Again, some of these vampires can be quite strong with the ability to fry a low level npc with a single thunderbolt or to decapitate yourself or NPCs. This seems to only happen when you are around to do something about it. Depending on your difficultly level, stats and gear you may find these encounters fairly simple and mundane or very annoying, causing multiple reloads to try and save named NPCs from slaughter. From personal experience playing on a variety of difficulty levels(apprentice thru legendary), you may want to make sure your character is quite strong and do the Dawnguard quest line relatively early in a play through so as to generally remove these attacks from the game. Hint:Lycanthropy eliminates the risk of accidentally becoming a vampire from fighting them, if you don't want to become one. There are of course shrines, potions of cure disease or Garlic Bread you can bake(Hearthfire DLC). Not a big fan of necklaces of Disease resist or immunity as thy take up an enchantment slot, but they can be useful in a pinch. You can also mostly avoid attacks by not being outside at night in a town or remaining indoors at night(though again, it is possible but unlikely for attacks to happen during broad daylight).
Another potential downside is the addition of new dragon types. In vanilla Skyrim, the most powerful common dragon is an Ancient Dragon with a little over 3k health, bite and tail attacks with 300 damage(on adept. varies with other difficulty multipliers) 200 damage wing attacks, 200 damage fireball or ice storm attacks, and 100 damage flame or frostbite attacks. The physical attacks can be reduced by armor and blocking, breath attacks by elemental and magical resistances. The new dragons(revered and legendary) have from around 3500 to 4400 hundred health with similar physical attacks as ancient dragons. Their fire and frost breath attacks are somewhat weaker, but they do have a new shout type called drain vitality(you can learn words to this shout too, but it works a little different for you as far as damage per second and duration). The shout drains health, magicka and stamina for 20 seconds(5/sec for revered, 7/sec for legendary). This is regardless of difficulty level or magic resistance. The only way to avoid it is to either dodge(if you have some distance as the shout doesn't move all that fast) or activating a ward(a simple lesser ward like the one you can get free at the start of the College quest line works, or the ward effect available on the Daedric artifact Spellbreaker). I believe you can use the become etherial shout as well, but I have not tested it with this shout.
This is another consideration not only for your character's well being, but that of NPCs should one of these new dragons attack a city or town(some low level NPCs only have around 100 health give or take). These dragons don't show up until you are fairly high level(like 75 or 80 for legendary, not sure about revered but they would appear at lower levels). Since I power level to 80+ in Helgen, most dragons I encounter are of the legendary variety(I do occasionally end up fighting weaker dragons). I wait to do dragon rising until I feel my character is sufficiently strong to handle legendary dragons in a relatively efficient manor, but I've had close calls in the wild on legendary difficulty(over 800 health, armor and resistance capped, swords that do over 1k damage each between physical attack and enchantments, bow over 1250 damage, no mods). If you don't really invest in magicka(say you max enchanting to make gear allowing free spell casting) you still can't cast at all if your magicka is dropped below zero, despite free cast gear. I get equilibrium from Labyrinthian so I can sacrifice some of my large health pool for magicka to be able to heal both myself and others if the need should arise.
Edit:forgot something else that can be a plus or a minus. While you are in the Soul cairn, you can do a fairly simple task. The reward is a horse you can summon. It last 60 seconds unless you hop on, then it lasts until either you hop off or if it should get killed by an enemy. You can summon it again and again. It doesn't have all that much health, but since you can summon it again that doesn't matter too much. If you summon Arvak(the horse's name) while owning a better than normal horse(say Frost or Shadowmere) then you may "lose" your better horse.